IEEE 802.3 industry standards for wired Ethernet utilize Reed-Solomon (RS) forward error correction (FEC) techniques for encoding data to control errors in data transmission over unreliable or noisy communication channels. The RS FEC techniques are used in the main stage in the receive path of the FEC layer, and are based on univariate polynomials over finite fields or Galois fields. These techniques use redundancy in the encoded data to enable a data receiver to detect and correct a limited number of errors in the received data. At the data receiver, error locations in the received data are found during decoding by finding roots of an error locator polynomial function. Traditional approaches to finding these roots use an exhaustive search on all elements of the finite field used by the RS encoding. This is the most computationally intensive and time-consuming stage of the RS decoding process, and therefore is a limiting factor for the decoding speed.